US2025035527A1PendingUtilityA1
Modeling optimized friction reducing compositions for downhole fluid compositions and methods of making and using
Est. expiryJul 5, 2043(~17 yrs left)· nominal 20-yr term from priority
Inventors:Asoke Kumar DeysarkarNikhil PatelChristopher DilleySandeep D. KulkarniNavneeth Kumar Korlepara
C09K 8/68C09K 8/882C09K 8/035C09K 8/88C09K 2208/28G01N 11/02
60
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Claims
Abstract
Mathematical equations for predicting a percent drag reduction (% DR) value for friction-reducing (FR) polymer compositions including various polymer properties and base fluid properties as the independent variables such as base fluid salinity, type of salts in the base fluid, molecular weight of the FR polymers, FR polymer concentrations, degrees of ionicity of the FR polymers, and percent sulfonation of AMPS-containing FR polymers.
Claims
exact text as granted — not AI-modified1 . An apparatus comprising:
an electronic device including a processing unit having a memory, one or more input devices, one or more output devices, one or more mass storage devices, an operating system, communication hardware and software, and software routines for calculating percent drag reduction (% DR) from friction-reducing (FR) polymer properties and base fluid properties, wherein the system is configured to:
receive input data comprising properties of a friction-reducing polymer composition and properties of an aqueous base fluid used to prepare a downhole fluid,
calculate a percent drag reduction (% DR) for a downhole fluid according to Equation (1):
%
DR
=
C
0
×
f
1
(
MW
)
×
f
2
(
[
MVI
]
)
×
f
3
(
[
DVI
]
,
%
S
)
×
f
4
(
[
FRP
]
)
(
1
)
wherein:
C 0 is a constant;
ƒ 1 is explicit function of friction-reducing (FR) polymer molecular weights;
ƒ 2 is explicit function of monovalent salt concentration in base fluid;
ƒ 3 is explicit function of two independent variables: divalent salt concentration of the base fluid and the percent AMPS units in the FR polymers;
ƒ 4 is explicit function of the FR polymer concentration; and
the following dependent variable:
% DR is estimated drag reduction of a downhole fluid; and
the following measurable independent variables:
MW is the polymer weight of the FR polymers to be added to the base fluid to form the downhole fluid;
% S is a measure of a percentage of AMPS units in the FR polymers to be added to the base fluid to form the downhole fluid;
[MVI] is the monovalent ion concentration in the base fluid;
[DVI] is the divalent ion concentration in the base fluid;
[FRP] is the FR polymer concentration to be added to the base fluid to form the downhole fluid; and
% S is a measure of a percentage of AMPS units in the FR polymers to be added to the base fluid to form the downhole fluid,
receive updated input data comprising properties of a friction-reducing polymer composition and properties of an aqueous base fluid in real-time or near real-time used to modify a composition of the friction-reducing polymer composition used in the downhole fluid,
modify the friction-reducing polymer composition based on the updated input data, and
repeat the receive updated input data and the modify the friction-reducing polymer composition until the downhole operation is stopped,
wherein the downhole fluid includes a downhole treating fluid or a downhole drilling fluid and
wherein the treating downhole fluids include slick water fracturing fluids, cross-linked fracturing fluids, proppant-containing, slick water fracturing fluids, proppant-containing, cross-linked fracturing fluids, high and low viscosity completion fluids, zone isolation fluids, or any other treating fluid.
2 . The apparatus of claim 1 , wherein the function of Equation (1) comprises the functional form of Equations (2) or (2a):
DR
=
C
0
×
[
1
-
(
1
e
(
C
MW
×
MW
)
)
]
×
[
1
-
(
C
MVI
×
[
MVI
]
)
]
×
[
1
+
∑
i
=
1
3
(
∑
j
=
0
3
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
]
×
[
∑
k
=
0
3
C
FRPk
[
FRP
]
k
]
(
2
)
DR
=
C
0
×
[
1
-
(
1
e
(
C
MW
×
MW
)
)
]
×
[
1
-
(
C
MVI
×
[
MVI
]
)
]
×
[
1
+
∑
i
=
1
2
(
∑
j
=
0
2
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
]
×
[
∑
k
=
0
2
C
FRPk
[
FRP
]
k
]
(
2
a
)
wherein:
% DR represents percent drag reduction of a downhold fluid,
C 0 represents a real number zeroth order constant,
MW is the molecular weight of the FR polymers,
C MW is a real number constant associated with the independent variable FR polymer molecular weight,
[MVI] is the concentration of monovalent metal ions in the base fluid,
C MVI is a real number constant associated with the independent variable [MVI],
[DVI] is the concentration of divalent metal ions in the base fluid,
% S is a measure of the amount of AMPS monomer units in the FR polymers,
C DVIij are real number constants associated with the independent variables [DVI] and % S,
[FRP] is the concentration of FR polymers,
C FRPk is a real number constant associated with the independent variable [FRP],
i is an integer counter ranging from 1 to 3 for Equation (2) or 1 to 2 for Equation (2a),
j is an integer counter ranging from 0 to 3 for Equation (2) or 0 to 2 for Equation (2a), and
k is an integer counter ranging from 0 to 3 for Equation (2) or 0 to 2 for Equation (2a).
3 . The apparatus of claim 1 , wherein the function ƒ 1 (MW) comprises the functional form of exponential functions of Equations (3) or (3a):
f
1
(
MW
)
=
1
-
(
1
e
(
C
MW
×
MW
)
)
(
3
)
f
1
(
MW
)
=
1
-
(
1
e
(
Z
MW
×
MW
20.5
)
)
(
3
a
)
wherein:
MW is the molecular weight of the FR polymers having a real numeric value between about 0.5 and about 25.00 MDa (mega Daltons), including any subrange or any specific value within the range, and
C MW is a real number constant having a value between about 0.0195 and about 1.9512, including any subrange or any specific value within the range, or
Z MW is a real number constant having a value between about 0.4 and 40.0 including any subrange or any specific value within the range.
4 . The apparatus of claim 1 , wherein the function ƒ 2 ([MVI]) may take the functional form of linear functions of Equations (4) or (4a):
f
2
(
[
MVI
]
)
=
1
-
(
C
MVI
×
[
MVI
]
)
(
4
)
f
2
(
[
MVI
]
)
=
1
-
(
Z
MVI
×
[
MVI
]
1
8
0
0
0
0
)
(
4
a
)
wherein:
[MVI] is the concentration of monovalent metal ions in the base fluid having a real numeric value between about 10 and about 250,000 ppm, including any subrange or any specific value within the range, and
C MVI is a real valued constant having a value ranging between about 5.556×10 −9 and 5.556×10 −7 , including any subrange or any specific value within the range, or
Z MVI having a real numeric value between about 0.001 and 0.100 including any subrange or any specific value within the range.
5 . The apparatus of claim 1 , wherein the function ƒ 3 ([DVI], % S) may take the functional form of polynomial functions of Equation (5) and (5a):
f
3
(
[
DVI
]
,
%
S
)
=
1
+
∑
i
-
1
3
(
∑
j
=
0
3
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
(
5
)
f
3
(
[
DVI
]
,
%
S
)
=
1
+
∑
i
-
1
2
(
∑
j
=
0
2
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
(
5
a
)
wherein:
[DVI] is the concentration of monovalent metal ions in the base fluid having a real numeric value between about 1 and about 100,000 ppm, including any subrange or any specific value within the range,
% S is a measure of the amount of AMPS monomer units in the FR polymers,
C DVI10 is a real number constant having a value between about −2×10 −6 and about −2×10 −4 ,
C DVI11 is a real number constant having a value between about 5×10 −8 and about 5×10 −6
C DVI12 is a real number constant having a value between about −8×10 −10 and about −8×10 −8
C DVI13 is a real number constant having a value less than ±1×10 −10 ,
C DVI20 is a real number constant having a value between about 2×10 −11 and about 2×10 −9
C DVI12 is a real number constant having a value between about 8×10 −13 and about 8×10 −11 ,
C DVI22 is a real number constant having a value between about 1×10 −11 and about 1×10 −12 , and
C DVI23 is a real number constant having a value less than ±1×10 −13 .
6 . The apparatus of claim 1 , wherein the function ƒ 4 ([FRP]) may take the functional form of a polynomial functions of Equation (6) and (6a):
f
4
(
[
FRP
]
)
=
∑
k
=
0
3
C
FRPk
[
FRP
]
k
(
6
)
f
4
(
[
FRP
]
)
=
∑
k
=
0
2
C
FRPk
[
FRP
]
k
(
6
a
)
wherein:
[FRP] is the concentration of FR polymers,
C FRP0 is a real number constant having a value between about 0.06 and about 6.00,
C FRP1 is a real number constant having a value between about 0.04 and about 4.00,
C FRP2 is a real number constant having a value between about −1.00 and about −0.01, and
C FRP3 is a real number constant having a value less than ±0.01.
7 . The apparatus of claim 1 , wherein the function of ƒ 3 comprises Equation (7):
f
3
(
dv
,
%
s
)
=
1
+
(
z
dv
,
1
×
C
dv
)
+
(
z
dv
,
2
×
C
dv
2
)
(
7
)
wherein
:
C
dv
=
ppm
of
CaCl
2
+
(
x
×
ppm
of
MgCl
2
)
,
(
7
a
)
z
dv
,
1
=
z
dv
,
1
,
S
.1
+
(
z
dv
,
1
,
S
.2
×
%
s
)
+
(
z
dv
,
1
,
S
.3
×
%
s
2
)
(
7
b
)
z
dv
,
1
,
S
,
1
is
1.3
×
1
0
-
1
3
,
z
dv
,
1
,
S
,
2
is
-
8.813
×
1
0
-
1
2
,
and
z
dv
,
1
,
S
,
3
is
2
.
6
9
9
7
1
×
1
0
-
1
0
z
dv
,
2
=
z
dv
,
2
,
S
.1
+
(
z
dv
,
2
,
S
.2
×
%
s
)
+
(
z
dv
,
2
,
S
.3
×
%
s
2
)
(
7
c
)
z
dv
,
2
,
S
,
1
is
-
8.03
×
1
0
-
9
,
z
dv
,
2
,
S
,
2
is
5
.
9
4
3
0
4
×
1
0
-
7
,
and
z
dv
,
2
,
S
,
3
is
-
2.3354
×
1
0
-
5
,
wherein:
polymer molecular weight in MDa ranges between about 0.5 and about 25,
percent of sulfonic acid groups (% s) in polymer in wt. % ranges between about 0.1 and about 45,
C pc (polymer concentration in ppt) ranges between about 0.1 and about 5,
C mv (monovalent salt concentration in ppm) between about 10 and about 250,000, and
C dv (divalent salt concentration in ppm) about 1 and about 100,000.
8 . The apparatus of claim 1 , wherein the aqueous base fluid properties include salinity, conductivity, pH, specific metal ions and/or metal salts, concentrations of the specific metal ions and/or metal salts, other ions and/or chemicals, ionicity, any other property of the aqueous base fluid, or any combination thereof.
9 . The apparatus of claim 1 , wherein the formation properties include formation temperature or temperature profile, formation pressure or pressure profile, formation geological structural properties, e.g., type of rock, shale, sand, etc., type and nature of natural fractures within the formation, extent of the formation to be treated, depth of penetration of the treating fluid, desired treating results, type of proppants to be used, type of proppant pillar formation, type of pumping format, pumping conditions such as pumping pressure, downhole fluid flow rate, pumping sequences, other formation properties, or any combination thereof.
10 . The apparatus of claim 1 , wherein the polymers friction-reducing polymers include at least 30% acrylamide, at least 40% acrylamide, at least 40% acrylamide, at least 50% acrylamide, at least 60% acrylamide, at least 70% acrylamide, at least 80% acrylamide, at least 90% acrylamide, or 100% acrylamide. It should be recognized that these ranges include all subranges such as 30% to 100% or any other range or any other at least percentage.
11 . A method implemented on an electronic device including a processing unit having a memory, one or more input devices, one or more output devices, one or more mass storage devices, an operating system, communication hardware and software, and software routines for calculating percent drag reduction (% DR) from friction-reducing (FR) polymer properties and base fluid properties, the method comprising:
receiving input values comprising properties of a friction-reducing polymer composition and properties of an aqueous base fluid used to prepare a downhole fluid, calculating a % DR value from a function having the form of Equation (1):
%
DR
=
C
0
×
f
1
(
MW
)
×
f
2
(
[
MVI
]
)
×
f
3
(
[
DVI
]
,
%
S
)
×
f
4
(
[
FRP
]
)
(
1
)
wherein:
C 0 is a constant;
ƒ 1 is explicit function of friction-reducing (FR) polymer molecular weights;
ƒ 2 is explicit function of monovalent salt concentration in base fluid;
ƒ 3 is explicit function of two independent variables: divalent salt concentration of the base fluid and the percent AMPS units in the FR polymers;
ƒ 4 is explicit function of the FR polymer concentration; and
the following dependent variable:
% DR is estimated drag reduction of a downhole fluid; and
the following measurable independent variables:
MW is the polymer weight of the FR polymers to be added to the base fluid to form the downhole fluid;
% S is a measure of a percentage of AMPS units in the FR polymers to be added to the base fluid to form the downhole fluid;
[MVI] is the monovalent ion concentration in the base fluid;
[DVI] is the divalent ion concentration in the base fluid;
[FRP] is the FR polymer concentration to be added to the base fluid to form the downhole fluid; and
% S is a measure of a percentage of AMPS units in the FR polymers to be added to the base fluid to form the downhole fluid,
receiving updated input data comprising properties of a friction-reducing polymer composition and properties of an aqueous base fluid in real-time or near real-time used to modify a composition of the friction-reducing polymer composition used in the downhole fluid,
modifying the friction-reducing polymer composition based on the updated input data, and
repeating the receiving updated input data and the modifying the friction-reducing polymer composition until the downhole operation is stopped,
wherein the downhole fluid includes a downhole treating fluid or a downhole drilling fluid and
wherein the treating downhole fluids include slick water fracturing fluids, cross-linked fracturing fluids, proppant-containing, slick water fracturing fluids, proppant-containing, cross-linked fracturing fluids, high and low viscosity completion fluids, zone isolation fluids, or any other treating fluid.
12 . The method of claim 11 , wherein, in the calculating step, the function of Equation (1) may take the functional form of Equations (2) and (2a):
DR
=
C
0
×
[
1
-
(
1
e
(
C
MW
×
MW
)
)
]
×
[
1
-
(
C
MVI
×
[
MVI
]
)
]
×
[
1
+
∑
i
=
1
3
(
∑
j
=
0
3
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
]
×
[
∑
k
=
0
3
C
FRPk
[
FRP
]
k
]
(
2
)
DR
=
C
0
×
[
1
-
(
1
e
(
C
MW
×
MW
)
)
]
×
[
1
-
(
C
MVI
×
[
MVI
]
)
]
×
[
1
+
∑
i
=
1
2
(
∑
j
=
0
2
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
]
×
[
∑
k
=
0
2
C
FRPk
[
FRP
]
k
]
(
2
a
)
wherein:
% DR represents percent drag reduction of a downhold fluid,
C 0 represents a real number zeroth order constant,
MW is the molecular weight of the FR polymers,
C MW is a real number constant associated with the independent variable FR polymer molecular weight,
[MVI] is the concentration of monovalent metal ions in the base fluid,
C MVI is a real number constant associated with the independent variable [MVI],
[DVI] is the concentration of divalent metal ions in the base fluid,
% S is a measure of the amount of AMPS monomer units in the FR polymers,
C DVIij are real number constants associated with the independent variables [DVI] and % S,
[FRP] is the concentration of FR polymers,
C FRPk is a real number constant associated with the independent variable [FRP],
i is an integer counter ranging from 1 to 3 for Equation (2) or 1 to 2 for Equation (2a),
j is an integer counter ranging from 0 to 3 for Equation (2) or 0 to 2 for Equation (2a), and
k is an integer counter ranging from 0 to 3 for Equation (2) or 0 to 2 for Equation (2a).
13 . The method of claim 11 , wherein, in the calculating step, the function ƒ 1 (MW) may take the functional form of exponential functions of Equations (3) or (3a):
f
1
(
MW
)
=
1
-
(
1
e
(
C
MW
×
MW
)
)
(
3
)
f
1
(
MW
)
=
1
-
(
1
e
(
Z
MW
×
MW
20.5
)
)
(
3
a
)
wherein:
MW is the molecular weight of the FR polymers having a real numeric value between about 0.5 and about 25.00 MDa (mega Daltons), including any subrange or any specific value within the range, and
C MW is a real number constant having a value between about 0.0195 and about 1.9512, including any subrange or any specific value within the range, or
Z MW is a real number constant having a value between about 0.4 and 40.0 including any subrange or any specific value within the range.
14 . The method of claim 11 , wherein, in the calculating step, the function ƒ 2 ([MVI]) may take the functional form of linear functions of Equations (4) or (4a):
f
2
(
[
MVI
]
)
=
1
-
(
C
MVI
×
[
MVI
]
)
(
4
)
f
2
(
[
MVI
]
)
=
1
-
(
Z
MVI
×
[
MVI
]
1
8
0
0
0
0
)
(
4
a
)
wherein:
[MVI] is the concentration of monovalent metal ions in the base fluid having a real numeric value between about 10 and about 250,000 ppm, including any subrange or any specific value within the range, and
C MVI is a real valued constant having a value ranging between about 5.556×10 −9 and 5.556×10 −7 , including any subrange or any specific value within the range, or
Z MVI having a real numeric value between about 0.001 and 0.100 including any subrange or any specific value within the range.
15 . The method of claim 11 , wherein, in the calculating step, the function ƒ 3 ([DVI], % S) may take the functional form of polynomial functions of Equation (5) and (5a):
f
3
(
[
DVI
]
,
%
S
)
=
1
+
∑
i
-
1
3
(
∑
j
=
0
3
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
(
5
)
f
3
(
[
DVI
]
,
%
S
)
=
1
+
∑
i
-
1
2
(
∑
j
=
0
2
C
DVIij
×
(
%
S
)
j
)
[
DVI
]
i
(
5
a
)
wherein:
[DVI] is the concentration of monovalent metal ions in the base fluid having a real numeric value between about 1 and about 100,000 ppm, including any subrange or any specific value within the range,
% S is a measure of the amount of AMPS monomer units in the FR polymers,
C DVI10 is a real number constant having a value between about −2×10 −6 and about −2×10 −4 ,
C DVI11 is a real number constant having a value between about 5×10 −8 and about 5×10 −6
C DVI12 is a real number constant having a value between about −8×10 −10 and about −8×10 −8
C DVI13 is a real number constant having a value less than ±1×10 −10 ,
C DVI20 is a real number constant having a value between about 2×10 −11 and about 2×10 −9
C DVI12 is a real number constant having a value between about 8×10 −13 and about 8×10 −11 ,
C DVI22 is a real number constant having a value between about 1×10 −11 and about 1×10 −12 , and
C DVI23 is a real number constant having a value less than ±1×10 −13 .
16 . The method of claim 11 , wherein, in the calculating step, the function ƒ 4 ([FRP]) may take the functional form of a polynomial functions of Equation (6) and (6a):
f
4
(
[
FRP
]
)
=
∑
k
=
0
3
C
FRPk
[
FRP
]
k
(
6
)
f
4
(
[
FRP
]
)
=
∑
k
=
0
2
C
FRPk
[
FRP
]
k
(
6
a
)
wherein
[FRP] is the concentration of FR polymers,
C FRP0 is a real number constant having a value between about 0.06 and about 6.00,
C FRP1 is a real number constant having a value between about 0.04 and about 4.00,
C FRP2 is a real number constant having a value between about −1.00 and about −0.01, and
C FRP3 is a real number constant having a value less than ±0.01.
17 . The method of claim 11 , wherein the the function of ƒ 3 comprises Equation (7):
f
3
(
dv
,
%
s
)
=
1
+
(
z
dv
,
1
×
C
dv
)
+
(
z
dv
,
2
×
C
dv
2
)
(
7
)
wherein
:
C
dv
=
ppm
of
CaCl
2
+
(
x
×
ppm
of
MgCl
2
)
,
(
7
a
)
z
dv
,
1
=
z
dv
,
1
,
S
.1
+
(
z
dv
,
1
,
S
.2
×
%
s
)
+
(
z
dv
,
1
,
S
.3
×
%
s
2
)
(
7
b
)
z
dv
,
1
,
S
,
1
is
1.3
×
1
0
-
1
3
,
z
dv
,
1
,
S
,
2
is
-
8.813
×
1
0
-
1
2
,
and
z
dv
,
1
,
S
,
3
is
2
.
6
9
9
7
1
×
1
0
-
1
0
z
dv
,
2
=
z
dv
,
2
,
S
.1
+
(
z
dv
,
2
,
S
.2
×
%
s
)
+
(
z
dv
,
2
,
S
.3
×
%
s
2
)
(
7
c
)
z
dv
,
2
,
S
,
1
is
-
8.03
×
1
0
-
9
,
z
dv
,
2
,
S
,
2
is
5
.
9
4
3
0
4
×
1
0
-
7
,
and
z
dv
,
2
,
S
,
3
is
-
2.3354
×
1
0
-
5
,
wherein:
polymer molecular weight in MDa ranges between about 0.5 and about 25,
percent of sulfonic acid groups (% s) in polymer in wt. % ranges between about 0.1 and about 45,
C pc (polymer concentration in ppt) ranges between about 0.1 and about 5,
C mv (monovalent salt concentration in ppm) between about 10 and about 250,000, and
C dv (divalent salt concentration in ppm) about 1 and about 100,000.
18 . The method of claim 11 , wherein the aqueous base fluid properties include salinity, conductivity, pH, specific metal ions and/or metal salts, concentrations of the specific metal ions and/or metal salts, other ions and/or chemicals, ionicity, any other property of the aqueous base fluid, or any combination thereof.
19 . The method of claim 11 , wherein the formation properties include formation temperature or temperature profile, formation pressure or pressure profile, formation geological structural properties, e.g., type of rock, shale, sand, etc., type and nature of natural fractures within the formation, extent of the formation to be treated, depth of penetration of the treating fluid, desired treating results, type of proppants to be used, type of proppant pillar formation, type of pumping format, pumping conditions such as pumping pressure, downhole fluid flow rate, pumping sequences, other formation properties, or any combination thereof.
20 . The method of claim 11 , wherein the polymers friction-reducing polymers include at least 30% acrylamide, at least 40% acrylamide, at least 40% acrylamide, at least 50% acrylamide, at least 60% acrylamide, at least 70% acrylamide, at least 80% acrylamide, at least 90% acrylamide, or 100% acrylamide. It should be recognized that these ranges include all subranges such as 30% to 100% or any other range or any other at least percentage.Join the waitlist — get patent alerts
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